The determination of the critical concentration for a dilute heisenberg ferromagnet from the low-energy spin waves

Murray, Galen

doi:10.1088/0370-1328/89/1/317

Cited by 30 publications

(4 citation statements)

References 9 publications

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“…Subsequently, Murray [11,12] studied a ferromagnetic Heisenberg system with a random arrangement of two different types of atom with spins S 1 and S 2 and different exchange couplings. She treated the low-frequency, long-wavelength limit (ka ≪ 1, k the wave vector magnitude, a the lattice constant) by combining a perturbation scheme with a variational calculation.…”

Section: Development Of Theoretical Approachesmentioning

confidence: 99%

“…She treated the low-frequency, long-wavelength limit (ka ≪ 1, k the wave vector magnitude, a the lattice constant) by combining a perturbation scheme with a variational calculation. This lead to spin-wave energies or a dispersion relation at low concentration of magnetic ions in the form E(k) = 2S J(ka) 2 φ(p), where S is the magnitude of the spin, J is the exchange integral and φ(p) is called a "stiffness coefficient", which only depends on a fraction p of magnetic atoms and the lattice structure [11,12], with φ(1) = 1. Murray's approximative calculations indicated that there is a region above the percolation threshold p c where ferromagnetism is unstable.…”

Section: Development Of Theoretical Approachesmentioning

confidence: 99%

“…In the aforementioned studies [9,11,12] including those of Kaneyoshi [15] and Edwards and Jones [16], the higher terms in the impurity concentration were ignored in the calculation of the Green function. Thereby, the validity of accuracy of the calculated concentration dependence of the stiffness coefficient φ(p) remained irresolute.…”

Section: Development Of Theoretical Approachesmentioning

confidence: 99%

“…Actually, the effect of disorder on magnetism is an old issue in diluted spin systems [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], albeit only during the last decade or so disorder effects in magnetic semiconductors have been considered. Most of the past experimental findings have been on antiferromagnetic materials [22,23] with some in certain ferromagnets [24].…”

Section: Introductionmentioning

confidence: 99%

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Spin-wave theory in a randomly disordered lattice: A Heisenberg ferromagnet

Weiss,

Massih

2022

Preprint

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Starting from the hamiltonian for the Heisenberg ferromagnet which comprise randomly distributed nonmagnetic ions as impurities in a Bravais lattice, we express the spin operators by means of the Dyson-Maleev transformation in terms of the Bose operators of the second quantization. Then by using methods of quantum statistical field theory, we derive the partition function and the free energy for the system. We adopt the Matsubara thermal perturbation method to a portion of the hamiltonian which describes the interaction between magnons and the stationary field of nonmagnetic ions. Upon averaging over all possible distributions of impurities, we express the free energy of the system as a function of the mean impurity concentration. Subsequently, we set up the double-time single particle Green function at temperature T in the momentum space in terms of magnon operators and derive the equation of motion for the Green function through the Heisenberg equation of motion and then solve the resulting equation. From this, we calculate the self-energy and then the spectral density function for the system. We apply the formalism to the case of the simple cubic lattice and compute the density of states, the spectral density function and the lifetime of the magnons as a function of energy for several values of the mean concentration of nonmagnetic ions in the ferromagnetic lattice. We calculate the magnon energy spectrum as a function of the average impurity concentration fraction c, which shows that for low lying states, the excitation energy increases continuously with c in the studied range 0.1 ≤ c ≤ 0.7. We also use the spectral density function to compute some thermodynamical quantities through the magnon occupation number. We have obtained closed form expressions for the configurationally averaged physical quantities of interest in a unified fashion as functions of the mean concentration of nonmagnetic impurities c to any order of c applicable below a critical percolation concentration c p . The quantities of interest comprise the thermodynamic potential (free energy), the spin-wave self-energy and the spectral density function from which other quantities can be derived.

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Section: Development Of Theoretical Approachesmentioning

confidence: 99%

Section: Development Of Theoretical Approachesmentioning

confidence: 99%

Section: Development Of Theoretical Approachesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spin-wave theory in a randomly disordered lattice: A Heisenberg ferromagnet

Weiss,

Massih

2022

Preprint

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Magnetic Excitations in Amorphous Ferromagnets

Continentino

Rivier

1979

Physica Status Solidi (b)

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The propagation of magnetic excitations in amorphous ferromagnets is studied from the point of view of the theory of random frequency modulation. It is shown that the spin waves in the hydrodynamic limit are well described by perturbation theory while the roton-like magnetic excitations with wave vector about the peak in the structure factor are not. A criterion of validity of perturbation theory is found which is identical to a narrowing condition in magnetic resonance.Nous Btudions la propagation des excitations magnktiques dans les solides amorphes ferromagnktiques du point de vue da la thkorie de modulation akatoire de frequence. Nous montrons que les ondes de spins dans la limite hydrodynamique sont bien dkcrites par la theorie de perturbation, e t que les excitations magnetiques rotoniques, de vecteurs d'onde prhs du maximum du facteur de structure, ne le sont pas. On obtient une condition de validit6 de la theorie de perturbation qui est identique A la condition de rbtrkcissement de la raie ("narrowing condition") dans la thkorie de resonance magn6tique.

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Determination of temperature of phase transition in magnetic alloys by branching theory methods

Men¹,

Sinitskii²

1978

Soviet Physics Journal

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The determination of the critical concentration for a dilute heisenberg ferromagnet from the low-energy spin waves

Cited by 30 publications

References 9 publications

Spin-wave theory in a randomly disordered lattice: A Heisenberg ferromagnet

Spin-wave theory in a randomly disordered lattice: A Heisenberg ferromagnet

Magnetic Excitations in Amorphous Ferromagnets

Determination of temperature of phase transition in magnetic alloys by branching theory methods

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